least common multiple
 

so, I was helping my daughter with some (unrelated to this) math homework and I got to thinking about LCMs. And I wondered what was the LCM for all the numbers 1 thru 9 (inclusive). That is, what is the smallest number that is evenly divisible by 1, 2, 3, 4, 5, 6, 7, 8, and 9. Obviously, we can get a common multiple of them by multiplying 1x2x3x4x5x6x7x8x9. But that wouldn't necessarily be the LEAST common. So then I started eliminating those that aren't necessary.

1 is obvious. everything is a multiple of 1.
2 can go because anything that is divisible by 4, 6 or 8 is also divisible by 2.
3 is out because of its multiples 6 and 9.
4 goes too, because of its multiple 8.

that leaves us with 5x6x7x8x9, which equal 15,120. After playing with the numbers a bit, I found that you can remove 6, leaving 5x7x8x9=2,520, which is divisible by 6.

and that's as far as I've gotten. I'm 99% sure that 2,520 is the LCM for 1 thru 9 inclusive.

am I right? have I made any mistakes?

You are indeed correct. The six disappears because it is 2x3, and 8 and 9 both take care of both. The important thing is the power to which each prime factor is raised to. I could attempt to explain, but wikipedia should suffice:

Least Common Multiples Explained

The "Alternative Method" applies to your situation more clearly, as the example given has more than 2 factors to consider.

cool...thanks mo